Odisha Home Secretary Asit Tripathy said normalcy has been restored in the violence-hit town.
There was report of a stray incident that occurred during curfew relaxation hours, but it was promptly handled by security personnel, he said.
Director General of Police K B Singh said the police have arrested 80 people and registered eight cases in connection with the arson and violence that took place in the town.
The curfew, which was imposed on Friday, was relaxed from 8 am to till 2 pm during the day to allow people to procure essential commodities and do their daily chores, Bhadrak Collector Gyana Ranjan Das said.
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He said the administration and security forces are keeping a close watch and the future course of action would be decided after a review of the situation in the town, where violence had erupted after some persons allegedly posted offensive remarks against Hindu deities on the social media.
People queued up at shops to purchase provisions, the police said adding the curfew would continue for some more time.
Social media platforms remained blocked after the state government restricted access to them in Bhadrak town and nearby areas for 48 hours from last night to prevent rumours from spreading, a senior official said.
State Chief Secretary A P Padhi, who has directed the police's crime branch to probe the rumours circulated through social media, said no rumour monger would be allowed to instigate people and escalate tension.
The team is seeking information from people to track miscreants spreading hate messages on social media. Strict action would be taken against them, Special Director General of Police (Crime) B K Sharma said.
The crime branch has registered a case in connection with the issue, senior officials said.
A senior official said Rapid Action Force (RAF) and Central Reserve Police Force (CRPF) personnel had yesterday staged flag march in sensitive areas.
Besides, three companies of RAF and two companies of CRPF, 35 platoons of police (around 1,200 personnel) have been deployed to maintain law and order in the town.
Violence had erupted in Bhadrak town on Thursday after a group staged a demonstration near the Town police station demanding immediate arrest of those involved in posting offensive remarks against Hindu deities on social media.
Though the district administration clamped prohibitory orders, tension persisted and fresh violence was reported on Friday despite a peace meeting.
The escalation in tension prompted the administration to impose curfew on Friday.
Meanwhile, leaders of political parties traded charges and indulged in blame game over the violence.
Singhdeo alleged that delayed response on the part of the administration led to the violence.
BJD leader Debasis Samantray said all steps were being taken as per the chief minister's instructions and the situation in Bhadrak is normal now.